How Do You Know? - Asking Questions with the Hiding Game
Players: A parent and as many kids as you want!
Math Ideas: Commutativity, decomposition, number families
Questions to Ask:
How do you know?
Commercial board games are great fun, but sometimes you just need a way to kill 10 minutes while dinner is cooking. In those situations, I like to pull out little games like the Hiding Game to start a conversation
How to Play
All you need for this game is a set of similar objects - pennies, LEGO bricks, goldfish, or whatever you'd like.
The game is simple. You put out a set of blocks or goldfish and ask your child to count them. Then you ask her to close her eyes while you hide some of the blocks. When she opens her eyes you ask "How many did I hide?"
Where's the Math?
The game is simple, but the mathematical ideas are not! By hiding some of the blocks, you've forced your child to find a quantity without being able to count it directly. If you started with six blocks and now your child can only see four, she has to think abstractly about the quantities of four and six in order to find the right answer.
Another idea that kids interact with in the game is the idea that two numbers add to the same sum, regardless of the order in which you add them. This is known as the commutative property of addition, and it seems utterly obvious to adults. If 3+2 is 5, then clearly 2+3 is also 5, right?
But kids don't know that yet. Just watch this video below of my son playing the Hiding Game with eight pieces.
Did you see that? When I take away two pieces, he gets the answer almost immediately. But when I leave those two and take the other six pieces, he sits and thinks for a full 30 seconds before getting the right answer. He needs to keep playing with this game to keep interacting with this concept.
Questions to Ask
Notice that in the video above, I always respond to his answers with "How do you know?" I do this all the time in my middle school math classes, and believe me, it drives kids crazy. They just want to know whether they got the answer right!
But asking your child to explain her reasoning is probably the most important aspect of playing math. You learn more about how your child is thinking, and they get accustomed to the idea that math makes sense and can be justified with reasoning. By the way, I ask this question just as often when my son or daughter gets the answer wrong. Often, they will correct themselves in the midst of their own explanation.
After my son explains his reasoning, I don't tell him that his answer is correct. I show him the blocks so that he can confirm the answer. Kids, especially young ones, just want to hear their parents tell them that they're right. But as a parent, I want my kids to know that I am not the gatekeeper of right and wrong in the world of math. They can prove to themselves whether the answer is right or wrong.
Finally, if you made it through this clip, you spent 30 seconds starting at a bunch of LEGO bricks while my son silently thought. If that felt long in the video, believe me, it felt interminable in person. But I didn't interrupt his thinking. Instead, I gave him the time he needed to process the question.
This practice is known as wait time in education circles, and it is the single hardest part of teaching. We just want to get our kids on the right path, but our impatience can short-circuit the learning process that our kids are on. Telling a child that 2+6 is the same as 6+2 might seem like good teaching, but it's much more effective to give your kids an experience that helps them learn that fact on their own.
I still don't think my son has fully grasped the idea of commutativity, but I'm just going to stay patient until he discovers it on his own. Until then, I'll keep hiding blocks and asking "How do you know?"